Chapter 8
WEALTH AND PRODUCTION
One of the recurring themes in the sustainability literature has been
the legitimacy of using an economic framework to account for natural
resources. Those critical of such an approach contend that wealth
accounting assumes that produced assets, such as human and physical
capital, can substitute for natural-resource assets on a dollar-for-dollar
basis. This, they argue, does not capture the limited degree to which such
substitution is possible. A loss of some natural capital, such as an entire
ecosystem, surely cannot be made up with an increase in physical capital if
the very basis of social existence and well-being are destroyed in the areas
affected by that system. This makes them skeptical of the kind of wealth
accounts we are constructing here.
While we cannot hope to disentangle the full set of issues embedded
in this line of reasoning, we can at least start by focusing on the degree
of substitutability between the different assets. Underlying any wealth
accounts is an implicit production function, which is a blueprint of the
combinations of different assets with which we can achieve a given level of
output. These blueprints are usually written as a mathematical function,
which describes the precise relationship between the availability of
different amounts of inputs, such as physical and human capital services,
and the maximum output they could produce. The substitutability
between inputs is then measured as an elasticity of substitution. In general
terms, this captures the ease with which a decline in one input can be
compensated by an increase in another, while holding output constant.
More precisely, it measures how much the ratio of two inputs (for
example, physical capital and land) changes when their relative price
changes (for example, the price of land goes up relative to the price of
capital).1 The greater the elasticity, the easier it is to make up for the loss
WHERE IS THE WEALTH OF NATIONS?
of one resource by using another. Generally, an elasticity of less than one
indicates limited substitution possibilities.
A commonly used production function, which implies elasticities of one
between the inputs, is the Cobb-Douglas form, written as:
Yt = At K α Lβ
(8.1)
Income or output (Y ) is expressed as a function of the levels of capital
input (K ), labor input (L), an exogenous technological factor (A) and
the parameters a and b, which give the returns to capital and labor
respectively. If the national production options could be captured by
such a function, with natural capital services included, it would have
considerable implications for sustainability. First, it would imply a degree
of substitutability between natural and produced capital that would
give some comfort to those who argue we can lose some natural capital
without seriously compromising our well-being. Related to that it would
validate the Hartwick rule, which states that when exploiting natural
resources, consumption can be sustained at its highest possible level if
net saving just equals the rent from exploiting those resources (Hartwick
1977; Hamilton 1995). The Hartwick rule is a useful sustainability policy
since it is open to monitoring. We can check whether or not it has been
adhered to.
Economists have devoted a considerable amount of effort to estimating
these elasticities for inputs such as capital, labor, and energy but not
natural resources. Although, starting in the 1970s, there were theoretical
studies that modeled neoclassical economic growth with nonproduced
capital, such as natural resources, as factors in production (Stiglitz 1974a, b;
Mitra 1978),2 the empirical estimation of the underlying production
functions was never carried out, largely because of a lack of data.
This chapter is a preliminary attempt in that direction. As mentioned
in the earlier chapters, a database of new wealth estimates has been
developed, including both produced and nonproduced capital—
renewable and nonrenewable resources and human resources—which
allows us to estimate a production function that includes the services from
these different resources as inputs. This chapter examines, therefore, the
economic relationship between total wealth and income generation and
takes advantage of the new wealth estimates to estimate a production
function based on a larger set of assets. Section 2 presents the estimation
of the production function. Section 3 concludes.
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CHAPTER 8. WEALTH AND PRODUCTION
Estimation of Nested CES Production Function
T
he estimation carried out here uses national-level data on gross national
income (GNI) or economic output and sees the extent to which
variations in GNI across countries, at any point in time, can be explained in
terms of the national availability of produced capital, human resources, and
natural resources (energy and land resources). A Cobb-Douglas production
function of the form shown above is not appropriate for this estimation
because it restricts the elasticity between factors to be one. In fact, one of our
objectives is to estimate the elasticity of substitution between factors or groups
of factors. A form that holds the elasticity constant but allows it to take values
different from one is the constant elasticity of substitution (CES) production
function. In particular, this chapter uses a nested CES production function.
For example, a two-level nested CES with three inputs takes the form:3
X = F [ X AB ( A, B ),C ]
(8.2)
where X is the gross output; A, B, and C are inputs; and XAB represents the
joint contribution of A and B to production. The first level of the estimation
involves A and B; while the second level models the production of output by
XAB and C. A special feature of the nested CES function is that the elasticity
of substitution between the first-level inputs, A and B, can be different from
the elasticity of substitution between the second-level inputs, XAB and C. In
other words, by placing natural resources and other inputs in different levels
of the function, we effectively allow for different levels of substitutability. So,
for example, natural assets may be critical (low substitutability) while other
inputs are allowed to be more substitutable among themselves.
There are several studies that have estimated the nested CES production
function between three or four production inputs, such as capital, labor,
energy, and nonenergy materials at the firm level (Prywes 1986; Manne and
Richels 1992; Chang 1994; Kemfert 1998; Kemfert and Welsch 2000).
A common interest among these studies is examining the capital-energy
substitution in manufacturing industries. For example, Manne and Richels
(1992) estimated the substitution possibilities between the capital and labor
nest and energy to be about 0.4; while Kemfert (1998) estimated the same
to be about 0.5. On the other hand, Prywes (1986) found the elasticity of
substitution between the capital and energy nest and labor to be less than 0.5.
103
WHERE IS THE WEALTH OF NATIONS?
In this chapter we use related variables to estimate aggregate national-level
production functions. The variables used are:4
•
Produced capital (K) is an aggregate of equipments, buildings, and
urban land.
•
Human capital (H) has two alternative measures—human capital,
which relates educational attainment with labor productivity (HE); or
intangible capital residual (HR), which is obtained as the difference
between a country’s total wealth and the sum of produced and natural
assets. Part of the intangible capital residual captures human capital in
the form of raw labor and stock of skills. For further discussion of this
variable and its rationale see chapters 2 and 7.
•
Production and net imports of nonrenewable energy resources (E)
includes oil, natural gas, hard coal, and lignite.5
•
Land resources (L) refers to the aggregated value of cropland,
pastureland, and protected areas. Land is valued in terms of the
present value of the income it generates rather than its market value.
The GNI and all inputs mentioned above are measured in per capita
values at 2000 prices and are taken at the national level for 208 countries.
GNI data are obtained from the World Development Indicators (World
Bank 2005). HE is derived based on the work by Barro and Lee (2000);
E is a flow measure and is obtained using the same data that underpin
the wealth estimates; while the remaining variables, K, HR, and L are the
components of wealth as described in chapter 2.
The relationships of the production inputs to income are expressed in
nested CES production functions described in the chapter annex. Three
different nested CES approaches are examined:
•
One-level function, with two inputs
•
Two-level function, with three inputs
•
Three-level function with four inputs
The combinations of the variables in the different CES approaches were
varied to further investigate any possible differences among substitution
elasticities for pairs of inputs.
The production function approach taken so far neglects an important
set of factors that influence differences in national income. These
104
CHAPTER 8. WEALTH AND PRODUCTION
relate to the efficiency with which productive assets are utilized and
combined, and include both institutional as well as economic factors.
In this study, we consider the following institutional indicators, which
capture the efficiency with which production can take place, as well
as economic indicators, which also capture the efficiency of economic
organization:
•
Institutional development indicators—indices on voice and
accountability (VA), political instability and violence (PIV),
government effectiveness (GE), regulatory burden (RB), rule of law
(RL); and control of corruption (CC). An increase in a given index
measures an improvement in the relevant indicator. Hence, they are
expected to have a positive impact on income and possibly growth
(Kaufmann and others 2005).6
•
Economic indicators—trade openness (TOPEN) is calculated as
the ratio of exports and imports to GDP (World Bank 2005); and
the country’s domestic credit to the private sector as proportion
of GDP (PCREDIT), which represents private sector investments
(Beck and others 1999).7
Two methods of incorporating the impact of these institutional and
economic indicators were investigated. The first method involved the
derivation of residuals from the regression of a nested CES production
function. The residuals are the part of income not explained by the wealth
components—physical capital, human capital, land resources, and energy
resources, and are regressed on the identified institutional and economic
indicators. By using this method, however, a statistically significant
correlation between the residuals and any indicator would imply that
relevant variables have been omitted in the estimation of the nested CES
production function. Thus, the estimated coefficients of the nested
CES production function derived earlier will be biased and inefficient
(Greene 2000). Hence another method is considered to be more
appropriate. The influences of the institutional and economic indicators
on income will be incorporated into the efficiency parameter of the
production function, A (see annex 2). Depending on the available data
for the variables of the nested CES production function, the number of
countries drops in the range of 67 to 93 countries. In the complete case
method, for a given nested CES approach, the reduction is caused by
considering only those countries that have nonmissing observations for
their corresponding dependent and explanatory variables.8
105
WHERE IS THE WEALTH OF NATIONS?
Regression Results
T
he nested CES production functions are estimated using a nonlinear
estimation method.9 The sample size in each CES approach differs
because countries with missing observations in any of the variables
had to be dropped. Table A8.1.1 in annex 1 shows the estimated
substitution elasticities corresponding to the case where human capital
is part of the measured intangible capital residual (HR). All statistically
significant substitution elasticity estimates have a positive sign, which is
encouraging.10 The lowest is that between K and E at 0.37 in the threelevel production function. It is also interesting to note that most of the
significant elasticities of substitution are close to one.
A second round of regressions was carried out using the other measure
of human capital that is related to schooling and labor productivity, HE.
Table A8.1.2 in annex 1 shows the statistically significant elasticities of
substitution, which also have a positive sign. An elasticity of substitution
approximately equal to one is likewise found for most of the nested
functions.
The results provide some interesting findings. First, there is no sign that
the elasticity of substitution between the natural resource (land) and
other inputs is particularly low. Wherever land emerges as a significant
input, it has an elasticity of substitution approximately equal to or greater
than one. Second, the HE variable performs better in the estimation
equations than the HR variable. Third, the best-determined forms, with
all parameters significant, are those using HE, involving four factors and
containing the combinations:
•
K, HE, and L are nested together and then combine with E, or
•
K, HE, and E are nested together and then combine with L.
It is hard to distinguish between these two versions, and so they are both
used in the further analysis reported below.
From the nested CES production function estimations, the elasticity
estimates of the institutional and economic indicators can be derived.
Table A8.1.3 and table A8.1.4 in annex 1 show the results for the
four-factor production functions [(K,HE,L)/E] and [(K,E,HE)/L] of
table A8.1.2, respectively. In both tables, the variables on trade openness
106
CHAPTER 8. WEALTH AND PRODUCTION
and private sector investment are found to be statistically significant. The
elasticity estimates of these two variables are not very different from each
other. The results imply that for every percent increase in trade openness,
gross national income per capita (GNIPC) increases by approximately
0.5 percent. None of the institutional indicators, on the other hand, has a
statistically significant elasticity estimate.11
Simulation
T
he predicted value of the dependent variable can be calculated by using
the estimated coefficient estimates of the production function and
the mean values of the explanatory variables. Through this method, we try
to predict what will happen to the economic output per capita (GNIPC)
if there is significant natural resource depletion. The natural resource
considered in this exercise is land resources (L); and the four-factor nested
CES production functions used are [(K,HE,L)/E] and [(K,E,HE)/L] of
table A8.1.2. Table A8.1.5 in annex 1 presents the predicted average
GNIPC, as well as the change in GNIPC given a reduction in the amount
of land resources, other things being equal. Based on the production
function [(K,HE,L)/E], economic output is reduced by 50 percent when
the amount of L declines by about 92 percent, while holding other variables
constant. For the production function [(K,E,HE)/L], on the other hand, it
takes a reduction in the amount of L by about the same percentage, other
things being equal, to halve the economic output relative to the baseline.
Conclusions
I
n this chapter, we looked at the potential for substituting between
different inputs in the generation of GNI. Among these are land
resources, one of the most important natural resources. The estimation
of a well-known production function form, which allows the elasticities
of substitution to be different from one, was carried out. The resulting
elasticities involving land resources (between L and other inputs
such as physical capital, human capital, and energy resources) were
107
WHERE IS THE WEALTH OF NATIONS?
generally around one or greater, which implies a fairly high degree of
substitutability. Moreover, it validates the use of a Hartwick rule of saving
the rents from the exploitation of natural resources if we are to follow a
maximum constant sustainable consumption path.
This result, not surprisingly, has many caveats. Land resources as
measured here include cropland, pastureland, and protected areas. Each
has been valued in terms of present value of the flow of income that it
generates. Such flows, however, underrepresent the importance of, for
example, protected areas, which provide significant nonmonetary services,
including ecosystem maintenance services that are not included. Further
work is needed to include these values, and if this were done, and if
the GNI measure were adjusted to allow for these flows of income, the
resulting estimates of elasticities of substitution might well change. We
intend to continue to work along these lines and to improve the estimates
made here.
Another shortcoming of the method applied here is the limited number
of factors included in the original estimation. Generating national income
depends not on the stock of assets, but on the amounts of the stocks that
are used in production and the way in which they are used. For physical
and human capital and land, we assume the rate of use is proportional to
the stock. That assumption should be improved on, to allow for different
utilization rates.
Finally, the chapter also examines how the institutional and economic
indicators affect the generation of GNI. Estimation results show that
income generation is significantly influenced by changes in trade openness
and private sector investment. The institutional indicators, however, have
no statistically significant impact on income generation.
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CHAPTER 8. WEALTH AND PRODUCTION
Annex 1 Tables
Table A8.1.1 Elasticities of Substitution ( σ̂ i ), Using Human Resources (HR)
Elasticity of substitution
σ̂ i
Inputs
Standard
error
R-squared
Adj. R-squared
Sample size
3.88E-10
0.9216
0.9131
93
2.02
0.9958
0.9951
78
0.9375
0.9290
93
0.9089
0.8916
70
0.87667
0.8533
70
0.3435
0.1911
70
0.9958
0.9951
78
0.9350
0.9200
70
A. Two factors (one-level CES production function)
1.00*
(1) K/HR
–0.48
(2) K/E
B. Three factors (two-level CES production function)
(1) (K,HR)/L
(2)
➢ K/HR
6.79
➢ (K,HR)/La
1.00*
4.33E-10
(K,HR)/E
➢ K/HR
–0.78
➢ (K,HR)/Ea
(3)
13.92
1.31
1.00*
5.37E-10
➢ K/E
0.65
0.69
➢ (K,E)/HRa
1.00*
3.96E-09
(K,E)/HR
C. Four factors (three-level CES production function)
(1) (K,HR,L)/E
➢ K/HR
(2)
–0.90
0.97*
0.01
➢ (K,HR,L)/E b
1.00*
5.46E-12
(K,HR,E)/L
➢ K/HR
(3)
0.70
➢ (K,HR)/La
–0.13
0.17
➢ (K,HR)/E a
0.93*
0.18
➢ (K,HR,E)/Lb
1.00*
6.52E-09
0.37*
0.20
(K,E,HR)/L
➢ K/E
➢ (K,E)/HRa
–0.64
➢ (K,E,HR)/L
b
1.00*
0.55
1.27E-09
Source: Authors.
Notes:
Legend: K=physical capital; HR=human capital (captures raw labor and stock of skills); L=land resources; E=energy
resources.
Inputs in parentheses imply that they are nested.
a. Two inputs in a nested function.
b. Three inputs in a nested function.
(*) denotes statistical significance at 5 percent level.
The elasticities of substitution and their corresponding standard errors are rounded off to the nearest hundredth.
109
WHERE IS THE WEALTH OF NATIONS?
Table A8.1.2 Elasticities of Substitution ( σ̂ i ), Using Human Capital
Related to Schooling (HE)
Elasticity of substitution
σ̂ i
Inputs
Standard
error
R-squared
Adj. R-squared
Sample size
0.9061
0.8942
81
0.9203
0.9076
81
0.8952
0.8742
67
0.7674
0.7209
67
0.9037
0.8081
67
0.9059
0.8828
67
0.9062
0.8831
67
A. Two factors (one-level CES production function)
1.00*
(1) K/HE
2.50E-08
B. Three factors (two-level CES production function)
(1) (K,HE)/L
➢ K/HE
1.01*
0.01
➢ (K,HE)/La
1.00*
2.23E-10
➢ K/HE
1.65*
0.12
➢ (K,HE)/Ea
1.00*
6.76E-11
(2) (K,HE)/E
(3) (K,E)/HE
➢ K/E
➢ (K,E)/HE
a
0.17
0.19
1.00*
8.22E-08
C. Four factors (three-level CES production function)
(1) (K,HE,L)/E
➢ K/HE
➢ (K,HE)/La
➢ (K,HE,L)/E
b
1.78*
0.11
1.14*
0.02
1.00*
2.52E-12
(2) (K,HE,E)/L
➢ K/HE
–8.55
12.61
➢ (K,HE)/E
0.48*
0.17
➢ (K,HE,E)/Lb
1.00*
4.60E-11
1.57*
0.37
0.92*
0.02
1.00*
6.41E-11
a
(3) (K,E,HE)/L
➢ K/E
➢ (K,E)/HEa
➢ (K,E,HE)/L
b
Source: Authors.
Notes:
Legend: K=physical capital; HE=human capital related to educational attainment and labor productivity; L=land
resources; E=energy resources.
Inputs in parentheses imply that they are nested.
a. Two inputs in a nested function.
b. Three inputs in a nested function.
(*) denotes statistical significance at 5 percent level; (**) at 10 percent level.
The elasticities of subtitution and their corresponding standard errors are rounded off to the nearest hundredth.
110
CHAPTER 8. WEALTH AND PRODUCTION
Table A8.1.3 Elasticity Estimates of the Economic and Institutional
Indicators, Using the [(K, HE, L)/E] Production Function
Variable
Elasticity
Standard error
t-statistic
TOPEN
0.47
0.10
4.53
PCREDIT
0.51
0.12
4.25
VA
0.01
0.04
0.28
PIV
–0.01
0.02
–0.28
GE
0.04
0.10
0.40
RB
0.03
0.07
0.39
RL
–0.07
0.10
–0.73
CC
0.01
0.09
0.17
Source: Authors.
Note: Legend: TOPEN=trade openness; PCREDIT=variable for private sector investment; VA=voice and
accountability; PIV=political instability and violence; GE=government effectiveness; RB=regulatory burden;
RL= rule of law; and CC=control of corruption.
Table A8.1.4 Elasticity Estimates of the Economic and Institutional
Indicators, Using the [(K, E, HE)/L] Production Function
Variable
Elasticity
Standard error
t-statistic
TOPEN
0.50
0.09
5.27
PCREDIT
0.51
0.11
4.83
VA
0.02
0.03
0.45
PIV
–0.01
0.02
–0.44
GE
0.06
0.09
0.62
RB
0.03
0.07
0.37
RL
–0.08
0.09
–0.86
CC
–0.02
0.08
–0.24
Source: Authors.
Note: Legend: TOPEN=trade openness; PCREDIT=variable for private sector investment; VA=voice and
accountability; PIV=political instability and violence; GE=government effectiveness; RB=regulatory burden;
RL=rule of law; and CC=control of corruption.
111
WHERE IS THE WEALTH OF NATIONS?
Table A8.1.5 Level of Gross National Income per Capita, Given
a Reduction in the Amount of Land
Reduction in the amount of land by
Prod. function
(K,HE,L)/E
Baseline*
$8,638.10
Difference from baseline**
(K,E,HE)/L
$9,096.20
Difference from baseline**
20%
50%
75%
92%
$8,068.84
$7,019.27
$5,774.25
$4,297.16
(–7%)
(–19%)
(–33%)
(–50%)
$8,540.27
$7,477.97
$6,147.62
$4,455.06
(–6%)
(–18%)
(–32%)
(–51%)
Source: Authors.
Notes:
*Predicted per capita GNI at the mean values of the explanatory variables.
**Rounded off to the nearest whole number.
Sample size of each production function = 67.
112
CHAPTER 8. WEALTH AND PRODUCTION
Annex 2 Three Different CES Approaches
1. A traditional CES production function with two inputs is written as:
(a) Physical capital (K) and human capital (H)
(
Y = A aK − β + bH − β
)
−1 β
(A.1)
(b) Physical capital (K) and energy resources (E)
Y = A(aK − β + bE − β )−1 β
(A.2)
where Y is the per capita gross national income. A is an efficiency
parameter. a and b are distribution parameters that lie between zero
and one and b represents the substitution parameter. The elasticity of
substitution (s) is calculated as: s
= (1/[1 +
b ]). Values of b must be
greater than –1 (a value less than –1 is economically nonsensical, although
it has been observed in a number of studies [Prywes 1986]). If b > –1, the
elasticity of substitution must, of course, be positive.
A, the efficiency parameter, is assumed to be a function of the economic
(TOPEN and PCREDIT ) and institutional indicators described in the
text. Two functional forms of A have been tried:
(c) A = e
λ1TOPEN + λ2 PCREDIT + λ3VA + λ4 PIV + λ5GE + λ6RB + λ7 RL + λ8CC
(A.3)
(d) A = λ1TOPEN + λ2 PCREDIT + λ3VA + λ4 PIV + λ5GE
+ λ6 RB + λ7 RL + λ8CC
(A.4)
and the second functional form of A was found to be more appropriate.
TOPEN means trade openness; PCREDIT is a variable for private sector
investment; VA, voice and accountability; PIV, political instability and
violence; GE, government effectiveness; RB, regulatory burden; RL, rule
of law; and CC, control of corruption. The scores for each institutional
indicator lie between –2.5 and 2.5, with higher scores corresponding to
better outcomes.
2. A two-level nested CES production function with three inputs is
investigated for three cases:
(a) K and H in the nested function, XKH is a substitute for land resources (L):
(
Y1 = A1  a1 b1K −α1 + (1 − b1 )H −α1

)
β1 α1
+ (1 − a1 )L− β1 

−1 β1
(A.5)
113
WHERE IS THE WEALTH OF NATIONS?
(b) K and H in the nested function, XKH is a substitute for energy
resources (E):
−1 β2
β2 α 2
Y 2 = A2  a2 b2 K −α 2 + (1 − b2 )H −α 2
+ (1 − a2 )E − β2 

(A.6)

(
)
(c) K and E in the nested function, XKE is a substitute for human
capital (H):
(
)
Y3 = A3  a3 b3 K 3 + (1 − b3 )E 3
+ (1 − a3 )H

where ai and bi are substitution parameters.
−α
−α
β3 α 3
− β3


−1 β3
(A.7)
3. A three-level nested CES production function with four inputs is
studied for these three cases:
(a) K, H, and L in the nested function, and E as a substitute for XKHL:
{[(
−α
−α
Y 4 = A4 a4 b4 c 4 K 4 + (1 − c 4 )H 4
+ (1 − b4 )L− ρ4
β 4 ρ4
]
)
}
ρ4 α 4
−1 β4
+ (1 − a4 )E − β4
(A.8)
(b) P, H, and E in the nested function, and L as a substitute for XKHE :
{[(
Y5 = A5 a5 b5 c5 K
+ (1 − b5 )E
− ρ5
)
] + (1 − a )L }
−α5
+ (1 − c5 )H
ρ5 α 5
−α5
β5 ρ5
− β5
−1 β5
5
(A.9)
(c) K, E, and H in the nested function, and L as a substitute for XKEH :
{[(
−α
−α
Y6 = A6 a6 b6 c 6 K 6 + (1 − c 6 )E 6
+ (1 − b6 )H − ρ6
β6 ρ6
]
)
ρ6 α 6
+ (1 − a6 )L−6 β6
−1 β6
}
(A.10)
where ai, ri, bi are substitution parameters; and 0 < ai, bi, ci < 1.
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CHAPTER 8. WEALTH AND PRODUCTION
The substitution elasticities for these CES approaches can be described
as follows:
σ αi = 1
1+ αi
Gives the elasticity of substitution between K and
H when i = 1,2,4,5
σ ρi = 1
1 + ρi
Gives the elasticity of substitution between K and E
when i = 1,6
Gives the elasticity of substitution between K/H
and L when i = 4
Gives the elasticity of substitution between K/H
and E when i = 5
σ βi = 1
1 + βi
Gives the elasticity of substitution between K/E and
H when i = 6
Gives the elasticity of substitution between K/H
and L when i = 1
Gives the elasticity of substitution between K/H
and E when i = 2
Gives the elasticity of substitution between K/E and
H when i = 3
Gives the elasticity of substitution between K/H/L
and E when i = 4
Gives the elasticity of substitution between K/H/E
and L when i = 5
Gives the elasticity of substitution between K/E/H
and L when i = 6
The nested CES production functions are estimated using the nonlinear
estimation method via the STATA program. The nonlinear estimation
program uses an iterative procedure to find the parameter values in
the relationship that cause the sum of squared residuals (SSR) to be
minimized. It starts with approximate guesses of the parameter values
(also called starting values), and computes the residuals and then the SSR.
The starting values are a combination of arbitrary values and coefficient
estimates of a nested CES production function. For example, the
starting values of equation (A.1) are arbitrary. A set of numbers is tried
until convergence is achieved. On the other hand, the starting values of
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WHERE IS THE WEALTH OF NATIONS?
equation (A.5) are based on the coefficient estimates of equation (A.1).
Next, it changes one of the parameter values slightly and computes again
the residuals to see whether the SSR becomes smaller or larger. The
iteration process goes on until there is convergence—it finds parameter
values that, when changed slightly in any direction, cause the SSR to
rise. Hence, these parameter values are the least squares estimate in the
nonlinear context.
Endnotes
1. Where prices are not defined, we measure the change in the ratio of the inputs resulting
from a change in the marginal rate at which one factor can be substituted for another
(Chiang 1984).
2. A bibliographical compilation of studies can be found in Wagner (2004). One
exception to the observation that there is little empirical work is Berndt and Field (1981),
who did look at limited natural resource substitution between capital, labor, energy, and
materials. The studies generally found low elasticities between capital and materials. They
did not, however, look at land as an input in the way we do here. Nor did they work with
national-level data.
3. This model makes the further assumption of homothetic weak separability for groups of
inputs. Homothetic weak separability means that the marginal rate of substitution between
inputs in a certain group is independent of output and of the level of inputs outside that
group (Chiang 1984).
4. Per capita dollar values at nominal 2000 prices are used.
5. For energy it would be inappropriate to take the stock value of the asset, as what is
relevant for production is the flow of energy available to the economy. This is given by
production plus net imports. With the other assets (K, H, and L) it is also the flow that
matters, but it is more reasonable to assume that the flow is proportional to the stock. We
do note, however, in the conclusions that even this assumption needs to be changed in
future work.
6. Data can be obtained from the website: http://www.worldbank.org/wbi/governance/pubs/
govmatters4.html.
7. Hnatkovska and Loayza (2004) use openness and credit as a measure of financial
depth, which they find to have a positive impact on growth. Data for this indicator
can be obtained from the following website: http://www.worldbank.org/research/projects/
finstructure/database.htm.
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8. An imputation method was tried to fill the missing values for some of the countries to
keep all 208 countries in the estimation. Most of the results, however, were not found
to be reasonable. For example, the imputed value of physical capital for a low-income
country turned out to be too high compared with the average value of physical capital
of its income group. Hence, the imputation method was not used since it poses more
problems in the estimates than using the complete case method.
9. See annex 2 for more details.
10. A negative elasticity of substitution is economically nonsensical—it implies a decline
in the availability of one input can be made up by a decline in the availability of other
factors. Nevertheless, some production function studies do find such negative values.
11. In the regression where the residuals are expressed as a function of the institutional
variables, we did find significant values for a few institutional variables, especially the
rule of law, which was encouraging as that variable also emerges as important in other
evaluations of intercountry differences in this study. Unfortunately, the result did not hold
when the more appropriate method was used.
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